Chapter 5: Problem 7
In Exercises \(7-12,\) evaluate the integral. $$\int_{-2}^{1} 5 d x$$
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In Exercises 55 and \(56,\) find \(K\) so that $$\int_{a}^{x} f(t) d t+K=\int_{b}^{x} f(t) d t$$ $$f(x)=\sin ^{2} x ; \quad a=0 ; \quad b=2$$
Group Activity Use the Max-Min Inequality to find upper and lower bounds for the value of \(\int _ { 0 } ^ { 1 } \frac { 1 } { 1 + x ^ { 4 } } d x\)
In Exercises 55 and \(56,\) find \(K\) so that $$\int_{a}^{x} f(t) d t+K=\int_{b}^{x} f(t) d t$$ $$f(x)=x^{2}-3 x+1 ; \quad a=-1 ; \quad b=2$$
True or False For a given value of \(n,\) the Trapezoidal Rule with \(n\) subdivisions will always give a more accurate estimate of \(\int_{a}^{b} f(x) d x\) than a right Riemann sum with \(n\) subdivisions. Justify your answer.
In Exercises \(27-40\) , evaluate each integral using Part 2 of the Fundamental Theorem. Support your answer with NINT if you are unsure. $$\int_{\pi / 4}^{3 \pi / 4} \csc x \cot x d x$$
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